cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A277972 a(1) = 1. a(n) is the smallest unlisted number, the name of which contains the first letter of the name of a(n-1) in English.

Original entry on oeis.org

1, 2, 3, 8, 5, 4, 14, 15, 24, 10, 12, 13, 16, 6, 7, 17, 26, 18, 9, 11, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 64, 60, 61, 62, 63, 65, 66, 67, 68, 69
Offset: 1

Views

Author

Ivan N. Ianakiev, Nov 07 2016

Keywords

Crossrefs

Cf. A277971.

Programs

  • Mathematica
    name[n_]:=IntegerName[n,"Words"];a[1]=1;
a[n_]:=a[n]=Module[{i=1}, While[Or[MemberQ[Table[a[k],{k,1,n-1}],i],
!StringContainsQ[name[i],StringTake[name[a[n-1]],1]]],i++ ];i];
a/@Range[69] (* Ivan N. Ianakiev, Dec 20 2021 *)

A281067 a(1) = 1; a(n) is the smallest natural number such that a(n) > a(n-1), and the name of a(n) in English starts with the letter a(n-1) ends with, and a(n) makes the sequence extendable.

Original entry on oeis.org

1, 8, 10, 19, 91, 801, 802, 1001, 8001, 8002, 100001, 800001, 800002, 1000000, 9000000, 9000001, 11000000, 19000000, 19000001, 80000000, 90000000, 90000001, 800000000, 900000000, 900000001, 8000000000, 9000000000, 9000000001, 11000000000, 19000000000, 19000000001, 80000000000, 90000000000, 90000000001
Offset: 1

Views

Author

Ivan N. Ianakiev, Jan 14 2017

Keywords

Comments

"a(n) makes the sequence extendable" means the name of a(n) does not end with any of the letters r, x, y and d.

Examples

			If a(5) were 90 (ninety, which ends with y), it would make the sequence finite. Therefore, a(5) has to be 91.

Crossrefs

Cf. A277971, A277972, A281068.

A281068 a(1) = 1. a(n) is the smallest natural number that is not already in the sequence such that the name of a(n) in English starts with the letter a(n-1) ends with, and a(n) makes the sequence extendable.

Original entry on oeis.org

1, 8, 2, 101, 11, 9, 18, 19, 91, 81, 82, 102, 103, 83, 85, 87, 92, 105, 88, 3, 89, 801, 802, 107, 93, 803, 805, 807, 95, 808, 10, 97, 98, 12, 809, 810, 99, 811, 901, 812, 813, 902, 108, 13, 903, 814, 905, 815, 907, 908, 21, 816, 909, 817, 910, 911, 912, 818, 913, 914, 915, 916, 917, 918, 919
Offset: 1

Views

Author

Ivan N. Ianakiev, Jan 14 2017

Keywords

Comments

"a(n) makes the sequence extendable" means the name of a(n) does not end with any of the letters r, x, y and d.

Examples

			If a(4) were 100 (one hundred, which ends with d), it would make the sequence finite. Therefore, a(4) has to be 101.

Crossrefs

Cf. A277971, A277972, A281067.

A282636 a(1) = 1. a(n) is the smallest natural number such that a(n) > a(n-1), the name of a(n) in (American) English ends with the letter a(n-1) starts with, and a(n) makes the sequence extendable.

Original entry on oeis.org

1, 2, 8, 9, 10, 28, 38, 88, 89, 91, 97, 107, 122, 132, 142, 152, 162, 172, 182, 192, 202, 208, 228, 238, 248, 258, 268, 278, 288, 298, 308, 328, 338, 348, 358, 368, 378, 388, 398, 808, 809, 812, 821, 823, 825, 829, 831, 833, 835, 839, 841, 843, 845, 849, 851, 853, 855, 859
Offset: 1

Views

Author

Ivan N. Ianakiev, Feb 20 2017

Keywords

Comments

"a(n) makes the sequence extendable" means the name of a(n) does not start with any of the letters f and s.

Examples

			38 is followed by 88 as 48, 58, 68 and 78 cannot make the sequence extendable.

Crossrefs

Cf. A277971, A277972, A281067, A281068, A282637.

Programs

  • Mathematica
    names = StringReplace[
   IntegerName /@ Range[1000], {"\[Hyphen]" -> "", " " -> ""}];
lst = {1}; next[n_] := next[n] =
  Module[{pos = Last[lst] + 1},
   While[
    Or[
     And[First[Characters[names[[Last[lst]]]]] !=
       Last[Characters[names[[pos]]]], pos <= Length[names]],
     MemberQ[{"f", "s"}, First[Characters[names[[pos]]]]] == True
     ],
    pos++
    ];
   AppendTo[lst, pos]
   ];
seq[n_] := Nest[next, 1, n]; seq[57]

A282637 a(1) = 1. a(n) is the smallest unlisted natural number whose name in (American) English ends with the letter a(n-1) starts with, and makes the sequence extendable.

Original entry on oeis.org

1, 2, 8, 3, 28, 38, 88, 9, 10, 98, 11, 12, 108, 22, 128, 32, 138, 82, 21, 148, 92, 13, 158, 102, 122, 132, 142, 152, 162, 172, 182, 192, 202, 168, 222, 178, 232, 188, 242, 198, 252, 208, 228, 238, 248, 258, 268, 278, 288, 298, 308, 328, 338, 348, 358, 368, 378, 388, 398, 808, 23, 828, 25, 838, 29, 848
Offset: 1

Views

Author

Ivan N. Ianakiev, Feb 20 2017

Keywords

Comments

"a(n) ... makes the sequence extendable" means the name of a(n) does not start with any of the letters f and s.

Examples

			38 is followed by 88 as 48, 58, 68 and 78 cannot make the sequence extendable.

Crossrefs

Cf. A277971, A277972, A281067, A281068, A282636.

Programs

  • Mathematica
    names = StringReplace[
   IntegerName /@ Range[1000], {"\[Hyphen]" -> "", " " -> ""}];
lst = {1}; next[n_] := next[n] =
  Module[{pos = Complement[Range[Length[names]], lst], i = 1},
   While[
    Or[
     And[
      First[Characters[names[[Last[lst]]]]] != Last[Characters[names[[pos[[i]]]]]],
      pos[[i]] <= Length[names]
      ],
     MemberQ[{"f", "s"}, First[Characters[names[[pos[[i]]]]]]] == True
     ],
    i++
    ];
   AppendTo[lst, pos[[i]]]
   ];
seq[n_] := Nest[next, 1, n]; seq[65]

A350217 a(1) = 1; a(n) > a(n-1) is the smallest number whose name in English does not contain the first letter of the name of a(n-1).

Original entry on oeis.org

1, 3, 4, 6, 8, 30, 100, 300, 400, 600, 800, 2000, 1000000
Offset: 1

Views

Author

Ivan N. Ianakiev, Dec 20 2021

Keywords

Crossrefs

Cf. A350218, A277971, A277972.

Programs

  • Mathematica
    name[n_]:=IntegerName[n,"Words"]; a[1]=1; a[n_]:=a[n]=Module[{i=a[n-1]+1}, While[
StringContainsQ[name[i],StringTake[name[a[n-1]],1]], i++ ]; i]; a/@Range[12]
  • Python
    from num2words import num2words
def n2w(n): return num2words(n).replace(" and", "")
def afind(limit):
    alst, aset = [1], {1}
    print(1, end=", ")
    while alst[-1] < limit:
        an = alst[-1] + 1
        avoid = n2w(alst[-1])[0]
        while an in aset or avoid in n2w(an): an += 1
        alst.append(an); aset.add(an)
        print(an, end=", ")
afind(100000) # Michael S. Branicky, Dec 20 2021

A350218 a(1) = 1. a(n) is the smallest unlisted number, the name of which does not contain the first letter of the name of a(n-1) in US English.

Original entry on oeis.org

1, 3, 4, 2, 5, 6, 8, 30, 7, 9, 12, 11, 32, 100, 10, 101, 13, 104, 15, 16, 14, 17, 18, 34, 105, 19, 33, 106, 20, 107, 23, 109, 25, 111, 26, 400, 21, 401, 22, 404, 27, 405, 28, 406, 29, 407, 31, 409, 36, 411, 37, 500, 38, 501, 39, 504, 60, 24, 505, 61, 35, 506, 62, 40, 63, 41, 66, 42, 67, 43
Offset: 1

Views

Author

Ivan N. Ianakiev, Dec 20 2021

Keywords

Crossrefs

Cf. A350217, A277971, A277972.

Programs

  • Mathematica
    name[n_]:=IntegerName[n,"Words"]; a[1]=1;
a[n_]:=a[n]=Module[{i=1}, While[ Or[ MemberQ[Table[a[k],{k,1,n-1}],i],
StringContainsQ[name[i],StringTake[name[a[n-1]],1]]], i++ ]; i];
a/@Range[70]
  • Python
    from num2words import num2words
def n2w(n): return num2words(n).replace(" and", "")
def aupton(terms):
    alst, aset = [1], {1}
    for n in range(2, terms+1):
        an = 1
        avoid = n2w(alst[-1])[0]
        while an in aset or avoid in n2w(an): an += 1
        alst.append(an); aset.add(an)
    return alst
print(aupton(70)) # Michael S. Branicky, Dec 20 2021
Showing 1-7 of 7 results.

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